# Simplifying Expressions (Collecting Like Terms) - Examples, Exercises and Solutions

The simplification of expressions consists of creating an equivalent expression written in a shorter and simpler way in which we combine all of the similar terms (collecting like terms).

For example, the expression:

$3+3+3+3+3+5X-3X$

After having simplified it, it would be:

$15+2X$

What we have done is created two groups of numbers and variables:
$3+3+3+3+3$ and $5X-3X$.

This can be simplified further, resulting in only two terms:$15+2X$

## examples with solutions for simplifying expressions (collecting like terms)

### Exercise #1

$18x-7+4x-9-8x=\text{?}$

### Step-by-Step Solution

To solve the exercise, we will reorder the numbers using the substitution property.

$18x-8x+4x-7-9=$

To continue, let's remember an important rule:

1. It is impossible to add or subtract numbers with variables.

That is, we cannot subtract 7 from 8X, for example...

We solve according to the order of arithmetic operations, from left to right:

$18x-8x=10x$$10x+4x=14x$$-7-9=-16$Remember, these two numbers cannot be added or subtracted, so the result is:

$14x-16$

$14x-16$

### Exercise #2

$7.3\cdot4a+2.3+8a=\text{?}$

### Step-by-Step Solution

It is important to remember that when we have numbers and variables, it is impossible to add or subtract them from each other.

We group the elements:

$7.3×4a + 2.3 + 8a =$

29.2a + 2.3 + 8a =

$37.2a + 2.3$

And in this exercise, this is the solution!

You can continue looking for the value of a.

But in this case, there is no need.

$37.2a+2.3$

### Exercise #3

$\frac{9m}{3m^2}\times\frac{3m}{6}=$

### Step-by-Step Solution

According to the laws of multiplication, we will simplify everything into one exercise:

$\frac{9m\times3m}{3m^2\times6}=$

We will simplify and get:

$\frac{9m^2}{m^2\times6}=$

We will simplify and get:

$\frac{9}{6}=$

We will factor the expression into a multiplication:

$\frac{3\times3}{3\times2}=$

We will simplify and get:

$\frac{3}{2}=1.5$

$0.5m$

### Exercise #4

$3x+4x+7+2=\text{?}$

### Video Solution

$7x+9$

### Exercise #5

$3z+19z-4z=\text{?}$

### Video Solution

$18z$

### Exercise #6

Are the expressions the same or not?

$20x$

$2\times10x$

Yes

### Exercise #7

Are the expressions the same or not?

$3+3+3+3$

$3\times4$

Yes

### Exercise #8

Are the expressions the same or not?

$18x$

$2+9x$

No

### Exercise #9

$x+x=$

### Video Solution

$2x$

### Exercise #10

$5+8-9+5x-4x=$

4+X

### Exercise #11

$5+0+8x-5=$

### Video Solution

$8X$

### Exercise #12

$11+5x-2x+8=$

19+3X

### Exercise #13

$7a+8b+4a+9b=\text{?}$

### Video Solution

$11a+17b$

### Exercise #14

$13a+14b+17c-4a-2b-4b=\text{?}$

### Video Solution

$9a+8b+17c$

### Exercise #15

$a+b+bc+9a+10b+3c=\text{?}$

### Video Solution

$10a+11b+(b+3)c$